Spanish prime minister Mariano Rajoy has said he is committed to reducing border controls with Gibraltar in a “constructive” 15-minute phone call with David Cameron.

The Prime Minister insisted the UK’s position on the Rock’s sovereignty would not change as the pair discussed ways to ease the current tensions over the territory.

A No 10 source said Mr Cameron told Mr Rajoy he did not want the row to “damage our bilateral relationship” and Foreign Secretary William Hague will lead further talks aimed at calming the situation.

Mr Cameron wrote on Twitter: “Constructive call with Spain’s PM Rajoy. I made clear my concerns re Gibraltar and that our position on sovereignty won't change.''

The Prime Minister’s intervention followed a formal protest by Britain’s ambassador to Spain over “disproportionate” checks at the border.

In his meeting with Spanish foreign secretary Gonzalo de Benito, ambassador Giles Paxman also sought an official explanation for Spanish threats to levy a charge on vehicles crossing the border and to close airspace.

A Foreign Office spokesman said: “Giles Paxman visited the Spanish secretary of state (for foreign affairs), Gonzalo de Benito, to formally protest at the disproportionate border checks at the weekend and to seek an explanation of foreign minister (Jose) Garcia-Margallo’s comments that he intends to target Gibraltar with future punitive measures.

“The ambassador reiterated that the UK would stand shoulder to shoulder with Gibraltar in face of threats from Spain.”

Spain was accused by Gibraltar’s chief minister of “sabre-rattling” after Mr Garcia-Margallo announced his proposals.

Mr Garcia-Margallo said the proceeds of a border fee could be used to help Spanish fishermen who have lost out because of damage to fishing grounds allegedly caused by Gibraltarian authorities following the creation of an artificial reef.

Gibraltar’s chief minister, Fabian Picardo, likened the behaviour to something from the Franco era or the regime in North Korea.

A Spanish government statement on the phone call made no mention of any concession over the border controls and stressed that the artificial reef was “unacceptable''.

Mr Rajoy “explained to his British counterpart that the development of controls at the border are due to the fulfillment of the duty to control illegal trafficking” and reiterated that the measures were “perfectly within the Schengen Borders Code, guided exclusively by the principles of randomness, proportionality and non-discrimination”.

The statement added: “The head of the Spanish government reiterated his will to find, as soon as is possible, a solution to the current situation created by the Gibraltar authorities, which has produced a deep unease and a great concern because it hurts the environment and fishing activity.”